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Schedule Computational Methods in Statistics with Applications

The course consists of two parts, which both will be given at the Department of Information Technology, Uppsala University. As a part of the work to be done within the course, a self-study part is included, to take place during Week 35 (August 29 - September 2) , 2011.

Preliminary!

Detailed time schedule

Week Date Topic(s) Time
Location
36 Sep 05 Introduction. General description of the course. Computational Statistics - the statistician's point of view and the numerical analyst's point of view 9:15-12:00    1412
    The statistical language R and Matlab - basics, short comparison. Computer lab exercises 13:15-17:00    1412
  Sep 06 Regression analysis, statistical concepts. Least Squares and QR factorization 9:15-12:00    1412
    Multiple regression. Normal equations vs QR factorization. Polynomial regression. 13:15-17:00    1412
  Sep 07 Regression analysis (cont). Rank deficiency. Singular value decomposition (SVD). Pseudo-inverses. Shrinkage methods. Cross validation 9:15-12:00    1412
    Numerical rank deficiency, collinearity. Application in pattern recognition: classification of handwritten digits (regression) 13:15-17:00    1412
  Sep 08 Regression problems with sparse data matrices. Sparse matrices - storage formats. Solving least squares problems with sparse matrices: direct and iterative methods. Computing the SVD 9:15-12:00    1412
    Handling sparse matrices in R and MATLAB. Regression. Some parallelization issues, related to data structure. 13:15-17:00    1412
  Sep 09 Graphs and their usage in Statistical applications (page-rank), regression trees and classification trees. Concepts of numerical stability. Floating point computations - short introduction, variance example 9:15-12:00    1412
    Floating point arithmetic - examples of loss of accuracy. Page ranking, the Google matrix 13:15-17:00    1412
37 Sep 12-16
 Work on Assignment (Part I) (not yet available)    
38 Sep 19 Principal Component Analysis. Eigenvalue computations (large scale, sparse, loss of orthogonality). Partial Least Squares. 9:15-12:00    1412
    Eigenvalue computations, applications 13:15-17:00    1412
  Sep 20 Random number generators. Markov chain Monte Carlo methods (MCMC) 9:15-12:00    1412
    MCMC application 13:15-17:00    1412
  Sep 21 Structured matrices in statistical applications. Structured covariance matrices - Toeplitz and circulant matrices, block matrices, Kronecker product matrices. Invariant and shift-invariant systems. Fourier matrices. 9:15-12:00    1412
    Generating test data with a pre-required structure. Testing some classical computational methods. 13:15-17:00    1412
  Sep 22 Parallel computing. Parallel Statistical computing 9:15-12:00    1412
    Parallel programming in R and Matlab, examples 13:15-17:00    1412
  Sep 23 Summary of the course material and sketch of new problems, methodologies, methods to be considered further 9:15-12:00    1412
39 Sept 26- 30
 Work on Assignment (Part II) (not yet available)    

 

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